Normal operators in 𝐶*-algebras without nice approximants

Hadwin, Don; Loring, Terry

doi:10.1090/S0002-9939-97-03734-9

Normal operators in $C*$-algebras without nice approximants
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by Don Hadwin and Terry A. Loring PDF

Proc. Amer. Math. Soc. 125 (1997), 159-161 Request permission

Abstract:

The second author constructed a separable direct limit $C^*$-algebra with real rank zero containing a normal element whose spectrum is the closed unit disk that is not the limit of normal elements in the limiting algebras, and is not a limit of normals in the algebra having finite spectrum. We use Fredholm index theory to modify and simplify this construction to obtain such examples that are not limits of any “nice” types of elements.

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